Alpha and Bravo: The Reversal in the Headline Rate
Two maintenance depots report annual figures. Depot Alpha completed 1,000 jobs: 100 urgent, of which 90 were on time, and 900 routine, of which 630 were on time. Depot Bravo completed 500 jobs: 400 urgent, of which 340 were on time, and 100 routine, of which 60 were on time. Both depots use identical definitions of urgent, routine and on time. Headquarters has one contract to award, and its rule is that the contract goes to the depot with the higher overall on-time rate. Bravo's commander says the headline rate settles the matter. Alpha's commander says the comparison is unfair because the mix of work differs.
1. Compute the overall and category on-time rates. Explain how the overall comparison can reverse the category comparisons.
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| Urgent | Routine | Overall | |
|---|---|---|---|
| Alpha | 90/100 = 90% | 630/900 = 70% | 720/1000 = 72% |
| Bravo | 340/400 = 85% | 60/100 = 60% | 400/500 = 80% |
Alpha is better in both categories, yet worse overall.
The cause is the workload mix. Urgent jobs are completed on time far more often at both depots, and Bravo's workload is 80% urgent (400/500) whereas Alpha's is 10% urgent (100/1000). Bravo's overall figure is dominated by its strongest category; Alpha's is dragged down by 900 routine jobs, which no depot completes well. The overall rate is measuring mix as much as performance.
2. Which depot performs better, and what should headquarters do with its award rule?
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On the evidence, Alpha performs better: it beats Bravo by 5 points on urgent work and 10 points on routine work, which are the only like-for-like comparisons available.
A standard-mix reweighting makes the gap explicit. Applying each depot's rates to an identical 50/50 mix:
- Alpha: 0.5 x 90 + 0.5 x 70 = 80%
- Bravo: 0.5 x 85 + 0.5 x 60 = 72.5%
Alpha leads by 7.5 points once mix is neutralised.
The judgement call: headquarters' written rule awards the contract to Bravo (80% vs 72%). Following the rule produces the wrong answer, and this is not a case for silent discretion. The right move is to apply the rule, flag the reversal in writing with the reweighted figures, and recommend the rule be amended to compare category rates or a standardised mix.
3. What assumption must hold for the headline comparison to be a fair measure of performance? Give one realistic fact that would break it.
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Assumption: the urgent/routine mix is outside the depot's control and is not itself a performance outcome. If so, weighting by mix punishes a depot for its job allocation, and the reversal is an artefact.
The assumption breaks if the mix reflects performance. Realistic breaker: urgent jobs are largely rework and repeat failures, and Alpha's 10 per cent urgent share exists because Alpha's preventive maintenance prevents failures that generate urgent work at Bravo. On that fact, Bravo's urgent-heavy workload is a symptom of poor performance, its 80% headline is flattered by high-volume repeat work, and Alpha is the stronger depot on both readings.
So the question to ask before awarding is not 'who is higher' but 'who decided the mix'.